Moment of Inertia of a Sphere

Calculate the moment of inertia of a sphere of radius R and mass M about an axis through the center of the sphere. Assume that the density of the sphere is not uniform, but is given by p_1 for 0 <= r <= R_1 and by p_2 for R_1 <= r <= R.

2. Relevant equations

Moment of inertia of a sphere:
I = 2/5*MR^2

3. The attempt at a solution

First, I calculated the total mass in terms of densities.
M = p_2 (4/3*pi*R^3 - 4/3*pi*R_1^3) + p_1(4/3*pi*R_1^3)
Then, I plugged M into the formula and simplified a little bit to get:
I = 8/15*pi*[(p_1-p_2)R_1^3 + p_2*R^5]
The correct answer, however has R_1^5 instead of R_1^3. What did I do wrong here?